Dynamic Network Optimal Tree

In the past, we study the minimum spanning tree problem of a network whose weights are static and determined. These assumptions are unrealistic in the real-world applications. So we need new ways to study the reality.In this paper, compared with the new problem and the old problems in the old research, we focus on the research of minimum spanning tree in a dynamic network. Our paper is divided in to three parts:(l)Introduce concepts of a static network. We also summarize algorithms to finding minimum spanning tree. Drawing on some ideas of a static network, we mainly do research for optimal tree of a time-varying network or a random network. For a time-varying network which's weights are continuous functions of time, we discuss on the relation about the minimum spanning tree at a moment and the minimum spanning tree of the moment's neighborhood and get the solution for the minimum spanning tree from the start node to the end node at a moment using the limited coverage theorem. The article examined the empirical distribution function for the sum of the random network's minimum spanning tree, and gave simulation ideas.(2)The article did researches about optimal tree issues from the side constraints and vertex degree constraints, and gave algorithms for optimal tree problem. (3) The article gave methods to choose the best model of network weights, and get the test statistic.